Analytical solution for one-dimensional radial flow caused by line source in porous medium with threshold pressure gradient

2019 ◽  
Vol 67 ◽  
pp. 151-158 ◽  
Author(s):  
Yang Zhou
Keyword(s):  
Porous Medium ◽  
Analytical Solution ◽  
Pressure Gradient ◽  
Line Source ◽  
Radial Flow ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
One Dimensional

scholarly journals Numerical Solution of a Moving Boundary Problem of One-Dimensional Flow in Semi-Infinite Long Porous Media with Threshold Pressure Gradient

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jun Yao ◽  
Wenchao Liu ◽  
Zhangxin Chen
Keyword(s):  
Porous Media ◽  
Partial Differential Equations ◽  
Pressure Gradient ◽  
Numerical Solution ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
One Dimensional

A numerical method is presented for the solution of a moving boundary problem of one-dimensional flow in semi-infinite long porous media with threshold pressure gradient (TPG) for the case of a constant flow rate at the inner boundary. In order to overcome the difficulty in the space discretization of the transient flow region with a moving boundary in the process of numerical solution, the system of partial differential equations for the moving boundary problem is first transformed equivalently into a closed system of partial differential equations with fixed boundary conditions by a spatial coordinate transformation method. Then a stable, fully implicit finite difference method is adopted to obtain its numerical solution. Finally, numerical results of transient distance of the moving boundary, transient production pressure of wellbore, and formation pressure distribution are compared graphically with those from a published exact analytical solution under different values of dimensionless TPG as calculated from actual experimental data. Comparison analysis shows that numerical solutions are in good agreement with the exact analytical solutions, and there is a big difference of model solutions between Darcy's flow and the fluid flow in porous media with TPG, especially for the case of a large dimensionless TPG.

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